# absolutely puzzled by absolute value

#### mnmathkid

##### New member
I looked around for help but 'still strugglin' with this one:

|x^2| + |y| = 1

everything I've seen doesn't have the square and that is throwing me off.

#### tkhunny

##### Moderator
Staff member
Have you noticed that x^2 >= 0, so that |x^2| = x^2?

#### mnmathkid

##### New member
tkhunny said:
Have you noticed that x^2 >= 0, so that |x^2| = x^2?
Oh! that looks right.... so I think you're saying that the ||'s arent needed and the problem is just like x^2 + |y| = 1 or, if I rewrite it, then a parabola like:

y = 1 - x^2 AND y = x^2 - 1

and I know how to figure out the domains with my TI so whoa, whoa!

#### Gene

##### Senior Member
Or
|y| = 1-x² is the same as
y=|1-x²|
They are both based on y=1-x² and it doesn't matter which side you do it to.

#### mnmathkid

##### New member
Gene said:
Or
|y| = 1-x² is the same as
y=|1-x²|
They are both based on y=1-x² and it doesn't matter which side you do it to.
thanks for that interesting twist! very cool.